Do I need a comma when I omit a word for stylistic reasons?

Sometimes when writing we omit words for stylistic reasons. This comma of omission is often seen when parallel structures are used, such as two sentences taking the same form.

Example: I loved playing tennis; my brother [loved] volleyball.

• Correct: I loved playing tennis; my brother, volleyball.
• Incorrect: I loved playing tennis; my brother volleyball.

We also need to include a comma of omission when we have removed a coordinating conjunction (usually "and"). This construction is fairly rare.

Example: I opened the boot [and] saw the spare tyre.

• Correct: I opened the boot, saw the spare tyre.
• Incorrect: I opened the boot saw the spare tyre.
• Correct: Carrie mimicked his tilted head, [and] then laughed.
• Incorrect: Carrie mimicked his tilted head [and] then laughed.